25. Electric Circuits 電路 Circuits, Symbols, & Electromotive Force 電路，符號，和電動勢 Series & Parallel Resistors 串聯和並聯電阻器 Kirchhoff’s Laws & Multiloop Circuits 基爾霍夫定律和多環路電路.

Presentation on theme: "25. Electric Circuits 電路 Circuits, Symbols, & Electromotive Force 電路，符號，和電動勢 Series & Parallel Resistors 串聯和並聯電阻器 Kirchhoff’s Laws & Multiloop Circuits 基爾霍夫定律和多環路電路."— Presentation transcript:

1 25. Electric Circuits 電路 Circuits, Symbols, & Electromotive Force 電路，符號，和電動勢 Series & Parallel Resistors 串聯和並聯電阻器 Kirchhoff’s Laws & Multiloop Circuits 基爾霍夫定律和多環路電路 Electrical Measurements 電的測量 Capacitors in Circuits 電路中的電容器

2 Festive lights decorate a city. 慶祝的燈泡點綴了一個城市。
If one of them burns out, they all go out. 如果其中一個燒了，全部都會熄掉。 Are they connected in series or in parallel? 它們是串聯還是並聯？

3 Electric Circuit = collection of electrical components connected by conductors.
電路 = 一些電元件由導體連在一起。 Examples 例 : Man-made circuits: flashlight, …, computers. 人做的電路：手電筒，… ，電腦。 Circuits in nature: nervous systems, …, atmospheric circuit (lightning). 大自然中的電路：神經系統，… ，大氣電路(閃電) 。

4 25.1. Circuits, Symbols, & Electromotive Force 電路，符號，和電動勢
Common circuit symbols 常見的電路符號 All wires ~ perfect conductors  V = const on wire 全部接線 ~ 完美導體  線上 V = 常數 Electromotive force (emf) = device that maintains fixed V across its terminals. 電動勢(emf) = 端點維持着固定 V 的元件。 E.g., batteries (chemical), 電池(化學作用) ， generators (mechanical), 發電機(機械性) ， photovoltaic cells (light), 光電壓電池(光)， cell membranes (ions). 細胞薄膜(離子) 。

5 no internal energy loss. 無內部能量消耗。
m ~ q Collisions ~ resistance 碰撞 ~ 電阻 g ~ E Lifting ~ emf 抬起 ~ 電動勢 Ideal emf 理想電動勢： no internal energy loss. 無內部能量消耗。 Energy gained by charge transversing battery = q E ( To be dissipated as heat in external R. ) 電荷在橫渡電池後獲得的能量 = q E ( 將在外部 R 內當熱來消耗掉。) Ohm’s law: 歐姆定律

6 GOT IT? 25.1. The figure shows three circuits. 圖示三個電路。
Which two of them are electrically equivalent? 那兩個的電性相當？

7 25.2. Series & Parallel Resistors 串聯和並聯電阻器
Series resistors 串聯電阻器 : I = same in every component 每個元件的 I 都一樣 Same q must go thru every element. 通過每個元件的 q都必需要一樣。  For n resistors in series: n 個串聯電阻器 Battery lifts charges 電池拉起電荷 Energy loss 耗能 Voltage divider 分壓器

8 Example 25.1. Voltage Divider 分壓器
A lightbulb with resistance 5.0  is designed to operate at a current of 600 mA. 一個電阻為 5.0  的燈泡是為了在 600 mA 的電流中運作而設計。 To operate this lamp from a 12-V battery, 如果要用一個 12 V 電池來操作這盞燈， what resistance should you put in series with it? 你應該用甚麼電阻和它串聯？ lightbulb 燈泡 Voltage across lightbulb = 燈泡兩端的電壓 Most inefficient 很無効率

9 GOT IT? Rank order the voltages across the identical resistors R at the top of each circuit shown, and give the actual voltage for each. 替下面各電路上方同樣的電阻器 R 兩端的電壓排序，並列出每個電壓。 In (a) the second resistor has the same resistance R, and 在 (a)中第二個電阻器的電阻也是 R 。 (b) the gap is an open circuit (infinite resistance). 在 (b)中的缺口代表開路 (電阻無限大) 。 6V 3V 0V

10 Real Batteries 實際的電池 Model of real battery = ideal emf E in series with internal resistance Rint . 實際電池的模型 = 理想 emf E 與內電阻 Rint 串聯。 I means V drop I Rint I 代表 V 下跌 I Rint  Vterminal < E

11 Example 25.2. Starting a Car 起動車子
Your car has a 12-V battery with internal resistance . 你的車子有一個 12-V 電瓶，其內電阻為 。 When the starter motor is cranking, it draws 125 A. 起動馬達轉動時會抽取 125 A 。 What’s the voltage across the battery terminals while starting? 電瓶兩極間的電壓在起動時是多少？ Battery terminals 電瓶兩極 Voltage across battery terminals = 電瓶兩極間的電壓 Typical value for a good battery is 9 – 11 V. 通常一個好電瓶的數值是 9 – 11 V 。

12 Parallel Resistors Parallel resistors 並聯電阻器 :
V = same in every component 每個元件的 V 都一樣  For n resistors in parallel : n 個並聯電阻器：

13 GOT IT? The figure shows all 4 possible combinations of 3 identical resistors. 圖示三個完全相同的電阻器的全部四種組合。 Rank them in order of increasing resistance. 按遞增電阻值替它們排序。 3R/2 3R R/3 2R/3 2 1 4 3

14 Analyzing Circuits Tactics 策略 :
Replace each series & parallel part by their single component equivalence. 把每個串和並聯部份以它們的單一相當元件取代。 Repeat 重覆。

15 Example 25.3. Series & Parallel Components 串和並聯元件
Find the current through the 2- resistor in the circuit. 求電路中通過 2- 電阻器的電流。 Equivalent of parallel 2.0- & 4.0- resistors: 2.0- 和 4.0- 並聯電阻器的相當值：  Equivalent of series 1.0-,  & 3.0- resistors: 1.0-,  和 3.0- 串聯電阻器的相當值： Total current is 總電流 Voltage across of parallel 2.0- & 4.0- resistors: 跨越 2.0- 和 4.0- 並聯電阻器的電壓： Current through the 2- resistor: 通過 2- 電阻器的電流：

16 GOT IT? The figure shows a circuit with 3 identical lightbulbs and a battery. 圖示由三個同樣燈泡和一個電瓶所組成的電路。 Which, if any, of the bulbs is brightest? 如果有的話，那個燈泡最亮？ What happens to each of the other two bulbs if you remove bulb C? 如果你把燈泡 C 拿掉，其他兩個燈泡會怎樣？ dimmer 暗些 brighter 亮些

17 25.3. Kirchhoff’s Laws & Multiloop Circuits 基爾霍夫定律和多環路電路
Kirchhoff’s loop law 基爾霍夫的環路定律： V = 0 around any closed loop 繞任何環路一周。 ( energy is conserved 能量守恆 ) Kirchhoff’s node law 基爾霍夫的節點定律: I = 0 at any node 每一節點. ( charge is conserved 電荷守恆 ) This circuit can’t be analyzed using series and parallel combinations. 這電路不能用串聯和並聯的組合來分析

18 Multiloop Circuits 多環路電路
Problem Solving Strategy 解題策略: INTERPRET 分析 ■ Identify circuit loops and nodes 找出電路的環路和節點。 ■ Label the currents at each node, assigning a direction to each. 為每個節點的電流命名，並設定方向。 DEVELOP 發展 ■ Apply Kirchhoff’s node law to all but one nodes. ( Iin > 0, Iout < 0 ) 把基爾霍夫的節點定律用於全部扣一個節點 ( Iin > 0, Iout < 0 ) 。 ■ Apply Kirchhoff’s loop law to all independent loops: 把基爾霍夫的環路定律用於全部獨立的環路： Batteries: V > 0 going from  to + terminal inside the battery. 電瓶：從  到 + 極 V > 0 。 Resistors: V =  I R going along +I. 電阻器：順 +I 走 V =  I R 。 Some of the equations may be redundant. 有些方程式可能是多餘的。

19 Example 25.4. Multiloop Circuit 多環路電路
Find the current in R3 in the figure below. 求圖中 R3 的電流。 Node 節 A: Loop 環 1: Loop 環 2:  

20 Application: Cell Membrane 應用：細胞膜
Hodgkin-Huxley (1952) circuit model of cell membrane (Nobel prize, 1963): 霍奇金-赫胥黎 (1952) 細胞膜的電路模型 ( 1963 年諾貝爾獎 ) ： Resistance of cell membranes 細胞膜的電阻 Membrane potential 細胞膜電位 Time dependent effects 與時間有關的効應 Electrochemical effects 電力化學効應

21 25.4. Electrical Measurements 電的測量
A voltmeter measures potential difference between its two terminals. 一個電壓(伏特)計可以量得它兩端點間的電位差。 Ideal voltmeter: no current drawn from circuit  Rm =  理想電壓計：不從電路抽取電流  Rm = 

22 Example 25.5. Two Voltmeters 兩個電壓計
You want to measure the voltage across the 40- resistor. 你要量 40- 電阻器上的電壓。 What readings would an ideal voltmeter give? 一個理想電壓計上的讀數為何？ What readings would a voltmeter with a resistance of 1000  give? 一個電阻 1000  的電壓計上的讀數為何？ (a) (b)

23 GOT IT? If an ideal voltmeter is connected between points A and B in figure, what will it read? 如果圖中A 和B 接了一個理想電壓計，它的讀數為何？ All the resistors have the same resistance R. 所有電阻器都有同樣的電阻 R。 ½ E

24 Ammeters 電流(安培)計 An ammeter measures the current flowing through itself. 一個電流(安培)計可以量得通過它本身的電流。 Ideal voltmeter: no voltage drop across it  Rm = 0 理想電流計： 它本身無電位差  Rm = 0

25 Ohmmeters & Multimeters 電阻計和萬用電表
An ohmmeter measures the resistance of a component. ( Done by an ammeter in series with a known voltage. ) 一個電阻計可以量得一個元件的電阻。 (以一個電流計和一個已知電壓串聯而成。) Multimeter: combined volt-, am-, ohm- meter. 萬用電表： 電壓，電流，和電阻計合而為一。

26 25.5. Capacitors in Circuits 電路中的電容器
Voltage across a capacitor cannot change instantaneously. 電容器兩端的電壓不能馬上改變。

27 The RC Circuit: Charging 阻容電路：充電時
C initially uncharged  VC = 0 開始時無電荷 開關 Switch closes at t = 0. 開關在 t = 0 時關上 VR (t = 0) = E  I (t = 0) = E / R C charging 充電中: VC   VR   I  Charging stops when I = 0. 充電到 I = 0 時停止。 VR  but rate  I  but rate  VC  but rate 

28   VC ~ 2/3 E I ~ 1/3 E/R Time constant 時間常數 = RC

29 The RC Circuit: Discharging 阻容電路：放電時
C initially charged to VC = V0 開始時已充電到 Switch closes at t = 開關在 t = 0 時關上 VR = VC = V  I 0 = V0 / R C discharging 放電中 : VC   VR   I  Disharging stops when I = V = 0. 放電到 I = V = 0 時停止。

30 Example 25.6. Camera Flash 相機閃光燈
A camera flash gets its energy from a 150-F capacitor & requires 170 V to fire. 一個相機閃光燈從一個 150-F 電容器取得能量，而且需要 170 V 才能閃。 If the capacitor is charged by a 200-V source through an 18-k resistor, 如果電容器透過一個 18-k 電阻器從一個 200-V 電源充電， how long must the photographer wait between flashes? 那個攝影師要隔多久才能再次閃光？ Assume the capacitor is fully charged at each flash. 假定每次閃光時電容器都充滿電。

31 RC Circuits: Long- & Short- Term Behavior 阻容電路：長和短時行為
For t << RC: VC  const,  C replaced by short circuit if uncharged. C 未充電時可以短路取替。  C replaced by battery if charged. C 已充電時可以電瓶取替。 For t >> RC: IC  0,  C replaced by open circuit. C 以斷(開)路取替。

32 Example 25.7. Long & Short Times 長和短時
The capacitor in figure is initially uncharged. 圖中的電容器開始時未充電。 Find the current through R 求通過 R1 的電流 the instant the switch is closed and 開關關上的一剎那。 a long time after the switch is closed. 開關關上後很長一段時間。 (a) (b)

33 GOT IT? 25.6. A capacitor is charged to 12 V 一個電容器充電到 12V
& then connected between points A and B in the figure, 然後接到圖中 A 和 B 點上 with its positive plate at A. (正板在 A)。 What is the current through the 2-k resistor 通過 2-k電阻器的電流為何 immediately after the capacitor is connected and (a) 接上電容器那一刻 a long time after it’s connected? (b) 接上後很久？ 6 mA 2 mA